While Shruti is re-building Kira's heater circuit, I looked up how to do one of these (i.e. what does a real EE say about how to build a current source?):
It turns out that there is an Analog Devices application note (AN-968) about this (as there usually is once we get tired of playing around and try to look up the right answer).
I've linked to the note and attached the recommended schematic for high current applications. We'll go ahead as is, but we'll make a PCB according to this App Note for the v3 circuit.